Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session HK: Non-Newtonian Flows I |
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Chair: Michael Shelley, Courant Institute, New York University Room: Tampa Marriott Waterside Hotel and Marina Meeting Room 4 |
Monday, November 20, 2006 2:00PM - 2:13PM |
HK.00001: Polymer-vortex interactions in confined flows Todd Weisgraber, David Clague, Berni Alder Drag reduction and delay of transition in bounded flows by the addition of small concentration of long chain polymers is well established, yet the underlying mechanism and a predictive model still remain elusive. Experiments and simulations reveal that the vortex structures in these flows are modified by the presence of the polymer. To further understand the details of these interactions and the dynamics of the polymer microstructure in a non-turbulent flow, we investigate the influence of a single-chain polymer on the formation and distribution of vorticity in a lid-driven cavity. We incorporate a FENE polymer chain model in a lattice-Boltzmann method for the fluid and examine the effect of chain length and extensibility on the initial flow transients. The relationship between the polymer relaxation and vortex formation time scales will also be discussed. [Preview Abstract] |
Monday, November 20, 2006 2:13PM - 2:26PM |
HK.00002: Coherent structures in plane Couette flow of viscoelastic fluids Alexander Morozov Newtonian fluids are known to exhibit turbulent behaviour at large enough Reynolds numbers. Recently, it has been discovered that flows of viscoelastic fluids in simple geometries become chaotic at arbitrary low Reynolds numbers, the so-called ``elastic turbulence,'' due to the presence of anisotropic elastic stresses. While Newtonian parallel shear flows, at least close to the transition, are believed to be organised around a few coherent structures -- exact solutions of the Navier-Stokes equations, the structure of the elastic turbulence remains unknown. Here we present a mean-field theory for the exact coherent structures in the presence of polymers. We calculate the region of existence of these structures for large Reynolds numbers and weak viscoelasticity which is relevant to the drag-reduction problem, and compare it to the recent numerical results of M. Graham \emph{et al.} We discuss the possibility that these solutions are connected to the solutions at low Reynolds numbers -- purely elastic coherent structures. [Preview Abstract] |
Monday, November 20, 2006 2:26PM - 2:39PM |
HK.00003: Viscoelastic nonlinear traveling waves and drag reduction in plane Poiseuille flow Wei Li, Michael Graham Nonlinear traveling waves that are precursors to laminar- turbulent transition and capture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. We present a study of the effect of polymer additives on the dynamical behavior of these ``exact coherent states'' (ECS) in the plane Poiseuille geometry using direct numerical simulation, focusing on Reynolds numbers slightly above transition. In experiments with a given fluid, Reynolds and Weissenberg numbers (Wi) are linearly related. In this situation, we study the dynamical behavior (i.e. birth, evolution and death) of viscoelastic ECS along some experimental paths (El=Wi/Re=const), which represent different flow behaviors as Re (and Wi) increases. These results are then compared with our previous static approach (i.e. finding steady states in a traveling wave frame), with regard to many key aspects of the turbulent drag reduction: delay in transition to turbulence; onset of drag reduction, diameter and concentration effects, and the nature of maximum drag reduction regime. [Preview Abstract] |
Monday, November 20, 2006 2:39PM - 2:52PM |
HK.00004: Beyond Drag Reduction: Bulk Turbulence in Dilute Polymer Solutions Nicholas Ouellette, Haitao Xu, Kelken Chang, Eberhard Bodenschatz Near boundaries, turbulent flows in solutions containing small amounts of long-chain polymers are known to show a significant reduction in turbulent drag compared to their Newtonian counterparts. We have investigated instead the effects of polymers on bulk turbulence, far away from any boundaries. We report measurements in an intensely turbulent water flow containing small amounts of a high molecular weight polyacrylamide using a versatile particle tracking technique capable of providing simultaneous Eulerian and Lagrangian data. We show that the Richardson cascade is strongly modified even with very small concentrations of polymers. We will present the effects of varying both the Reynolds number and the polymer concentration. This work was supported both by the National Science Foundation and by the Max Planck Society. [Preview Abstract] |
Monday, November 20, 2006 2:52PM - 3:05PM |
HK.00005: On the computation of viscoelastic Dean vortices Gilmar Mompean, Laurent Thais, Lionel Helin Since the pioneering study by Dean (Proc. Roy. Soc. London, Ser. A, 1928), it is known that the Newtonian flow in a curved channel exhibits transverse recirculations at ``Dean'' numbers beyond the critical value of 36. More recently, Joo and Shaqfeh (Phys. Fluids A, 1991, 1992) extended Dean's original work for viscoelastic fluids through a linear stability analysis. This work reports on numerical simulations of the three-dimensional viscoelastic flow of Oldroyd-B and Phan-Thien-Tanner fluids in a curved channel. The full three-dimensional momentum equations are solved in general orthogonal coordinates with a staggered finite volume numerical method. The conservative advective terms are discretized with a quadratic upwind scheme (QUICK). The time advancement of the solution follows from an explicit projection method. The Adams-Bashforth level 2 scheme is used to evaluate advection, curvature and viscous terms. The overall formulation is second order accurate in space and time. Results will be presented for various levels of inertia and elasticity, showing that Dean vortices can be induced at lower Dean numbers than observed in the Newtonian case. [Preview Abstract] |
Monday, November 20, 2006 3:05PM - 3:18PM |
HK.00006: Mixing in a Simple Viscoelastic Flow Becca Thomases, Michael Shelley Recent experiments have shown that low Reynolds number viscoelastic flows exhibit complicated flow patterns which include increased flow resistance and high levels of mixing. To better understand these phenomena we study numerically the 2D Oldroyd-B viscoelastic model at low Reynolds number. A background force is used to create a periodic cell with four-roll mill vortical structure around a hyperbolic fixed point. We consider both steady and time-periodic forcing. For low Weissenberg (\textit{Wi}) number the elastic stresses are bounded and slaved to the forcing, with mixing confined to small sets near the hyperbolic point. At larger \textit{Wi} an analog to the coil-stretch transition occurs, yielding large stresses and stress gradients concentrated on sets of small measure, perhaps indicating the development of singularities. ~The flow then becomes very sensitive to perturbations in the forcing and there is a transition to global mixing in the fluid. [Preview Abstract] |
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